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Ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption.

RLWE is more properly called Learning with Errors over Rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization and discrete logarithm problem have served as the base for public key cryptography since the early 1980s. An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem may be reducible to the NP-hard shortest vector problem (SVP) in a lattice.

(source: Wikipedia)